Third, the range (REF ) for the scale of lepton number
breaking is optimal for leptogenesis [1]} (for
a recent review, see Davidson:2008bu). If
(i) leptogenesis is generated by the decays of the lightest singlet
neutrino \(N_1\) , and (ii) the masses of the singlet neutrinos are
hierarchical, \(M_1/M_{2,3\ldots }\ll 1\)  , and (iii) the temperature
when leptogenesis occurs is high enough, \(T_\text{LG}>10^{12}\) ,
so that flavour effects are unimportant, then
there is an upper bound on the CP asymmetry in \(N_1\)  decays
[2]}:
\(|\epsilon _{N_1}|\le \frac{3}{16\pi }\frac{M_1(m_3-m_2)}{v^2}.\) 
